Inflator Definition

Defining an Inflator

The inflator capability in Abaqus/Explicit is suited for modeling the flow characteristics of inflators used for airbag systems. You must associate the inflator definition with a name. You specify the reference node of the fluid cavity that the inflator will fill with gas. A single fluid cavity can have any number of inflators.

Defining the Inflator Property

The inflator property defines the mass flow rate and temperature as a function of inflation time either directly or by entering tank test data. It also defines the mixture of gases entering the fluid cavity. You must associate the inflator property with a name. This name can then be used to associate a certain property with an inflator definition.

Specifying the Gas Temperature and Mass Flow Rate Directly

The temperature and the mass flow rate of the gas entering the fluid cavity can be given directly as functions of inflation time. Enter a table of mass flow rate and temperature versus inflation time.

Using Tank Test Data

The mass flow rate and the temperature of the gas entering the fluid cavity can be determined by the results of a tank test. In the test the inflator is discharged into a closed, fixed volume tank, and the time history of pressure in the tank is measured. The inflator mass flow rate can then be calculated from the pressure history using the equations of gas dynamics. For an ideal gas, conservation of energy for an adiabatic process is given by

{\dot{m}}_{t a n k} c_{v} θ_{t a n k} + m_{t a n k} c_{v} {\dot{θ}}_{t a n k} = {\dot{m}}_{i n} c_{p} (θ_{i n} - θ^{Z}),

where $θ$ is the temperature, $θ^{Z}$ is the absolute zero on the temperature scale being used, and the subscripts $i n$ and $t a n k$ refer to quantities in the inflator and the rigid tank, respectively. Using mass balance

{\dot{m}}_{t a n k} = {\dot{m}}_{i n},

and the equation of state for an ideal gas with constant volume gives

{\dot{p}}_{t a n k} V_{t a n k} = R ({\dot{m}}_{t a n k} θ_{t a n k} + m_{t a n k} {\dot{θ}}_{t a n k}) .

The mass flow rate can be found by combining the above equations

{\dot{m}}_{i n} = \frac{{\dot{p}}_{t a n k} V_{t a n k}}{γ R (θ_{i n} - θ^{Z})},

where $γ$ is the ratio of the constant pressure heat capacity, $c_{p}$ , and the constant volume heat capacity, $c_{v}$ :

γ = \frac{c_{p}}{c_{v}} .

To calculate the mass flow rate using the results of a tank test, enter a table of tank pressure and inflator temperature versus inflation time, and specify the volume of the tank.

Using the Dual Pressure Method

If both the inflator pressure, ${\tilde{p}}_{i n}$ , and tank pressure, $p_{t a n k}$ , time history curves can be measured during a tank test, the inflator mass flow rate and temperature can then be calculated using the assumption of isentropic flow (Wang and Nefske, 1988). The mass flow rate through the inflator orifice can be described by

{\dot{m}}_{i n} = C A \frac{{\tilde{p}}_{i n},}{\sqrt{R (θ_{i n} - θ^{Z})}} C_{t a n k},

where C is the discharge coefficient, A is the effective area, and the coefficient $C_{t a n k}$ is determined by assuming choked or sonic flow as

C_{t a n k} = {(\frac{2}{γ + 1})}^{\frac{1}{γ - 1}} \sqrt{\frac{2 γ}{γ + 1}} .

Comparing the expression for inflator mass flow rate obtained in a rigid tank with that given above, the inflator temperature is given by

θ_{i n} - θ^{Z} = \frac{1}{R} {(\frac{{\dot{p}}_{t a n k} V_{t a n k}}{γ C A C_{t a n k} {\tilde{p}}_{i n}})}^{2},

and the inflator mass flow rate is

{\dot{m}}_{i n} = \frac{γ {(C A C_{t a n k} {\tilde{p}}_{i n})}^{2}}{V_{t a n k} {\dot{p}}_{t a n k}} .

To calculate the inflator mass flow rate and temperature using the dual pressure method, enter a table of tank pressure and inflator pressure versus inflation time; and specify the volume of the tank, the effective area, and the discharge coefficient. The tank volume and effective area must be specified. The discharge coefficient has a default value of 0.4.

Specifying the Inflator Pressure and Mass Flow Rate Directly

You can enter a table of the mass flow rate and inflator pressure versus inflation time and specify the effective area and discharge coefficient. The gas temperature in the inflator will be calculated by using the assumption of isentropic flow. The effective area must be specified. The discharge coefficient has a default value of 0.4.

Specifying the Gas Mixture

To define the inflator gas mixture, specify the number of gas species used for the inflator, and enter a list of names of fluid behaviors and a table of the mass fraction or molar fraction of the species. The mass fraction or molar fraction of the species may be a function of inflation time. The sum of the mass fractions or molar fractions for the species should be equal to one at any given time.

Activating the Inflator Definition

Inflation does occur unless the inflation definition is activated in an analysis step.

Relating Inflation Time to Analysis Time

Inflator property definition consists of specifying tables of gas variables versus inflation time. In Abaqus/Explicit the inflation time, $t_{i n}$ , is related to the value of an amplitude curve $f (t)$ by

t_{i n} = \int_{0}^{t} f (t) d t .

Typically the amplitude variation is a step function stepping from zero to one at the time the airbag should be deployed. This amplitude variation has the effect of offsetting the inflation time from the analysis time.

Modifying the Mass Flow Rate

If the mass flow rate is prescribed directly in the inflator property definition, you can modify it by specifying an amplitude definition during a step. However, if the mass flow rate is calculated by using tank test data or the dual pressure method, the amplitude definition will be ignored.

Activation in Multiple Steps

By default, when you modify the activation of a fluid inflator definition or activate a new fluid inflator definition, all existing fluid inflator activations in the step remain. When modifying an existing activation, all applicable parameters must be respecified.

Activated inflator definitions remain active in subsequent steps unless deactivated. You can choose to deactivate all fluid inflator definitions in the model and optionally reactivate new ones. If you deactivate any fluid inflator definition in a step, all fluid inflator definitions must be respecified.

References

Wang, J. T., and O. J. Nefske, “A New CAL3D Airbag Inflation Model,” SAE paper 880654, 1988.